On the existence of non-free totally reflexive modules

Abstract

For a standard graded Cohen-Macaulay ring $S$, if the quotient $S/(\underline{x})$ admits non-free totally reflexive modules, where $\underline{x}$ is a system of parameters consisting of elements of degree one, then so does the ring $S$. As an application, we consider the question of which Stanley-Reisner rings of graphs admit non-free totally reflexive modules.

References in corpus (2)

• The radius of a subcategory of modules
• Modules of G-dimension zero over local rings with the cube of maximal ideal being zero

Cited by in corpus (1)

• On Gorenstein fiber products and applications